Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Readable signature
Prime(p)Exact expansion
~(p = 1) /\ forall a b. p = a * b -> a = 1 \/ b = 1This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.
Definition neighborhood
Depends on conservative definitions
none
Used by conservative definitions
All transitive conservative prerequisites
none
Used by theorem statements or local proof propositions
TS0005 prime_mod_four_one_minus_one_square_exists TS0006 prime_mod_four_one_bounded_minus_one_square_exists TS0008 prime_mod_four_one_divisible_two_square_norm_exists TS0009 prime_mod_four_one_bounded_divisible_two_square_norm_exists TS000C prime_is_not_natural_square TS000E prime_floor_square_strictly_below_prime TS000F prime_floor_bounded_coordinate_square_strict TS000H prime_floor_bounded_two_square_norm_below_double TS000K prime_floor_bounded_divisible_norm_represents_prime TS000Y prime_floor_affine_residue_grid_exists TS000Z prime_floor_affine_residue_grid_collision TS001M prime_floor_decoded_affine_collision_represents_prime TS001N prime_floor_affine_grid_collision_represents_prime TS001O prime_mod_four_one_is_sum_of_two_squares TS0020 prime_is_two_or_odd TS0021 prime_mod_four_trichotomy TS0024 prime_divisible_two_square_norm_unit_coordinate_yields_negative_one_root TS0025 three_mod_four_prime_has_no_negative_one_root TS0026 three_mod_four_prime_norm_divisor_forces_second_coordinate TS0027 three_mod_four_prime_divides_two_square_norm_divides_both TS0028 prime_is_two_squares_iff_two_or_one_mod_four TS002O prime_two_or_one_mod_four_is_sum_of_two_squares TS002P beta_all_prime_entry_is_prime TS002Q beta_admissible_prime_factor_product_is_two_square TS002S beta_grouped_prime_square_factor_product_is_two_square TS002V positive_number_with_admissible_prime_divisors_is_two_square TS002W prime_divisor_of_prime_forces_equality TS002X distinct_prime_power_valuation_zero TS002Z even_positive_prime_valuation_has_square_divisor TS0030 prime_square_divisibility_forces_suffix_prime_divisor TS0031 beta_sorted_prime_prefix_divisor_equals_bounded_last TS0032 even_valuation_sorted_terminal_prime_has_equal_predecessor TS003B prime_mod_four_good_or_three TS003C all_bad_prime_even_two_square_sufficiency_bounded TS003D positive_number_with_even_bad_prime_valuations_is_two_square TS003E nonzero_two_square_iff_even_three_mod_four_prime_valuations TS003F two_square_iff_zero_or_even_three_mod_four_prime_valuations TS003I prime_power_valuation_square_even TS003N three_mod_four_prime_two_square_norm_extracts_squared_factor TS003O three_mod_four_prime_nonzero_two_square_norm_extracts_nonzero_quotient TS003R three_mod_four_prime_nonzero_norm_positive_valuation_extracts TS003S prime_square_times_nonzero_strictly_increases TS003T three_mod_four_prime_two_square_norm_valuation_even_bounded TS003U three_mod_four_prime_two_square_norm_valuation_even TS003V three_mod_four_prime_represented_nonzero_valuation_evenGrand-campaign planning vocabulary
Locate Prime in the global campaign vocabulary →
Reviewed Prime corresponds to blueprint Prime with checked argument positions [0].
The global atlas describes planning vocabulary and does not itself certify a definition or theorem. The reviewed expansion and conservative dependency DAG on this page are the actual family-local reading definitions.